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<a href="_lasso_regression_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       LASSO Regression</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * This program demonstrates LASSO regression for the identification</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * of sparse coefficient vectors.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * </span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * </span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \date        2013</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> *</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> *</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * </span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * </span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * </span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> * </span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="comment"> *</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="comment"> */</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;<a class="code" href="_data_distribution_8h.html">shark/Data/DataDistribution.h</a>&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_squared_loss_8h.html">shark/ObjectiveFunctions/Loss/SquaredLoss.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &lt;<a class="code" href="_lasso_regression_8h.html">shark/Algorithms/Trainers/LassoRegression.h</a>&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#include &lt;fstream&gt;</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="keyword">using namespace </span>std;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="keyword">class </span>TestProblem : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_labeled_data_distribution.html" title="A LabeledDataDistribution defines a supervised learning problem.">LabeledDataDistribution</a>&lt;RealVector, RealVector&gt;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>{</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    TestProblem(<span class="keywordtype">size_t</span> informative, <span class="keywordtype">size_t</span> nnz, <span class="keywordtype">size_t</span> dim)</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    : m_informative(informative)</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    , m_nnz(nnz)</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    , m_dim(dim)</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    { }</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_labeled_data_distribution.html#ace4a2b81e54f0944d241b92a54f1a4c2" title="Generates a single pair of input and label.">draw</a>(RealVector&amp; input, RealVector&amp; label)<span class="keyword"> const</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="keyword">    </span>{</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        input.resize(m_dim);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        input.clear();</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        label.resize(1);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        <span class="comment">// we have one informative component per example</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="keywordtype">double</span> g = <a class="code hl_function" href="namespaceshark_1_1random.html#a972c5f7f031612a130aa077fc9136a9f" title="Draws a number from the normal distribution with given mean and variance by drawing random numbers fr...">random::gauss</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="keywordtype">size_t</span> i = <a class="code hl_function" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666" title="Draws a discrete number in {low,low+1,...,high} by drawing random numbers from rng.">random::discrete</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>, std::size_t(0), m_informative-1);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>        input(i) = g;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        label(0) = g;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <span class="comment">// the rest is non-informative</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> n=1; n&lt;m_nnz; n++)</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>            <span class="keywordtype">size_t</span> i = <a class="code hl_function" href="namespaceshark_1_1random.html#aa64d4174eaf7111b03e0504eaa56b666" title="Draws a discrete number in {low,low+1,...,high} by drawing random numbers from rng.">random::discrete</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>, m_informative, m_dim-1);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            input(i) = <a class="code hl_function" href="namespaceshark_1_1random.html#a972c5f7f031612a130aa077fc9136a9f" title="Draws a number from the normal distribution with given mean and variance by drawing random numbers fr...">random::gauss</a>(<a class="code hl_variable" href="namespaceshark_1_1random.html#ab5c1547eee483974d008d43f621a2234">random::globalRng</a>);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        }</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    <span class="keywordtype">size_t</span> m_informative;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="keywordtype">size_t</span> m_nnz;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    <span class="keywordtype">size_t</span> m_dim;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>};</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span> </div>
<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="_lasso_regression_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">   86</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="_datasets_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv)</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>{</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>    <span class="comment">// Define a test problem with 10 out of 1000 informative</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment">// components. Each instance contains one informative and</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>    <span class="comment">// 49 noise components. 10000 instances are drawn.</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>    TestProblem prob(10, 50, 1000);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>    cout &lt;&lt; <span class="stringliteral">&quot;generating 100000 points ...&quot;</span> &lt;&lt; flush;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">RegressionDataset</a> data = prob.generateDataset(100000);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>    cout &lt;&lt; <span class="stringliteral">&quot; done.&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    <span class="comment">// Set the regularization parameter.</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>    <span class="comment">// For this problem the LASSO method identifies the correct</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="comment">// subset of 10 informative coefficients for a large range</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="comment">// of parameter values.</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>    <span class="keywordtype">double</span> lambda = 1.0;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>    <span class="comment">// trainer and model</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>    <a class="code hl_class" href="classshark_1_1_linear_model.html" title="Linear Prediction with optional activation function.">LinearModel&lt;&gt;</a> model;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    <a class="code hl_class" href="classshark_1_1_lasso_regression.html" title="LASSO Regression.">LassoRegression&lt;&gt;</a> trainer(lambda);</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>    <span class="comment">// train the model</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>    cout &lt;&lt; <span class="stringliteral">&quot;LASSO training ...&quot;</span> &lt;&lt; flush;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>    trainer.<a class="code hl_function" href="classshark_1_1_lasso_regression.html#acf451db20a82eef8547629c28db9db4e" title="Train a linear model with LASSO regression.">train</a>(model, data);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>    cout &lt;&lt; <span class="stringliteral">&quot; done.&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>    <span class="comment">// check non-zero coefficients</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>    RealMatrix m = model.<a class="code hl_function" href="classshark_1_1_linear_model.html#ad16f3372ed0f7b3aa3c13c5519c7f6a4" title="return a copy of the matrix in dense format">matrix</a>();</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>    <span class="keywordtype">size_t</span> nnz = 0;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>    <span class="keywordtype">size_t</span> correct = 0;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>    <span class="keywordtype">size_t</span> wrong = 0;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j=0; j&lt;m.size2(); j++)</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>    {</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">if</span> (m(0, j) != 0.0)</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        {</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>            nnz++;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>            <span class="keywordflow">if</span> (j &lt; 10) correct++;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <span class="keywordflow">else</span> wrong++;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>    }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>    cout &lt;&lt; <span class="stringliteral">&quot;solution statistics:&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>    cout &lt;&lt; <span class="stringliteral">&quot;  number of non-zero coefficients: &quot;</span> &lt;&lt; nnz &lt;&lt; endl;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>    cout &lt;&lt; <span class="stringliteral">&quot;  correctly identified coefficients: &quot;</span> &lt;&lt; correct &lt;&lt; endl;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>    cout &lt;&lt; <span class="stringliteral">&quot;  wrongly identified coefficients: &quot;</span> &lt;&lt; wrong &lt;&lt; endl;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>}</div>
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